Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
Correct Answer
$6858
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5400 × 3% × 9
= $5400 ×3/100 × 9
= 5400 × 3 × 9/100
= 16200 × 9/100
= 145800/100
= $1458
Thus, Simple Interest = $1458
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1458
= $6858
Thus, Amount to be paid = $6858 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5400
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 9)
= $5400 + ($5400 ×3/100 × 9)
= $5400 + (5400 × 3 × 9/100)
= $5400 + (16200 × 9/100)
= $5400 + (145800/100)
= $5400 + $1458 = $6858
Thus, Amount (A) to be paid = $6858 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $162 × 9 = $1458
Thus, Simple Interest (SI) = $1458
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1458
= $6858
Thus, Amount to be paid = $6858 Answer
Similar Questions
(1) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(5) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?